Editing Graphic matroid (section)

{{Use American English|date = January 2019}}
{{Short description|Matroid with graph forests as independent sets}}
[[File:Graphic matroid of C4.svg|thumb|upright=1.3|The '''graphic matroid''' of the [[cycle graph]] {{mvar|C{{sub|4}}}}, which is the [[uniform matroid]] <math>U{}^3_4</math>. More generally, the graphic matroid of {{mvar|C{{sub|n}}}} is <math>U{}^{n-1}_{n}</math>.<ref>
{{cite book
 | last = Welsh
 | first = D. J. A.
 | year = 2010
 | title = Matroid Theory
 | publisher = Courier Dover Publications
 | page = 10
 | isbn = 9780486474397
}}</ref>]]

In the mathematical theory of [[Matroid theory|matroid]]s, a '''graphic matroid''' (also called a '''cycle matroid''' or '''polygon matroid''') is a [[matroid]] whose independent sets are the [[tree (graph theory)|forests]] in a given finite [[undirected graph]]. The [[dual matroid]]s of graphic matroids are called '''co-graphic matroids''' or '''bond matroids'''.<ref>{{harvtxt|Tutte|1965}} uses a reversed terminology, in which he called bond matroids "graphic" and cycle matroids "co-graphic", but this has not been followed by later authors.</ref> A matroid that is both graphic and co-graphic is sometimes called a '''planar matroid''' (but this should not be confused with matroids of rank 3, which generalize planar point configurations); these are exactly the graphic matroids formed from [[planar graph]]s.